Some simple assumptions about prior ignorance, and the idea that a sticiently arresting contrast in the likelihoods of evidence will elicit belief that one proposition is at least as belief-worthy as another, lead to a partial ordering of propositions without the use of any hind of prior probability. The partial ordering is mt a posterior probability distribution, but does share some intuitively pleasing properties of a probability, such as complementarity. Deciding the order (if any) between two disjunctions depends only on the highest likelihood disjunct in each, and so query handling in partitioned domains is efficient. In the event that an ordinary probability distribution is required for coherent decision making one can be quickly calculated from the partial order.

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